On 5/22/2012 10:56 AM, Joseph Knight wrote:

On Tue, May 22, 2012 at 7:36 AM, Stephen P. King<stephe...@charter.net <mailto:stephe...@charter.net>> wrote:On 5/21/2012 6:26 PM, Russell Standish wrote:snipHi Russell, I once thought that consistency, in mathematics, was the indication of existence but situations like this make that idea a point of contention... CH and AoC <http://en.wikipedia.org/wiki/Axiom_of_choice> are two axioms associated with ZF set theory that have lead some people (including me) to consider a wider interpretation of mathematics. What if all possible consistent mathematical theories must somehow exist?Joel David Hamkins introduced the "set-theoretic multiverse" idea(link <http://arxiv.org/abs/1108.4223>). The abstract reads:"The multiverse view in set theory, introduced and argued for in thisarticle, is the view that there are many distinct concepts of set,each instantiated in a corresponding set-theoretic universe. Theuniverse view, in contrast, asserts that there is an absolutebackground set concept, with a corresponding absolute set-theoreticuniverse in which every set-theoretic question has a definite answer.The multiverse position, I argue, explains our experience with theenormous diversity of set-theoretic possibilities, a phenomenon thatchallenges the universe view. In particular, I argue that thecontinuum hypothesis is settled on the multiverse view by ourextensive knowledge about how it behaves in the multiverse, and as aresult it can no longer be settled in the manner formerly hoped for."

Hi Joseph,

`Thank you for this comment and link! Do you think that there is a`

`possibility of an "invariance theory", like Special relativity but for`

`mathematics, at the end of this chain of reasoning? My thinking is that`

`any form of consciousness or theory of knowledge has to assume that`

`there is something meaningful to the idea that knowledge implies agency`

`<http://en.wikipedia.org/wiki/Agency_%28philosophy%29> and intention`

`<http://plato.stanford.edu/entries/intention/>...`

Its one reason why Bruno would like to restrict ontology to machines, or at most integers - echoing Kronecker's quotable "God made the integers, all else is the work of man".I understand that, but this choice to restrict makes Bruno's Idealism even more perplexing to me; how is it that the Integers are given such special status, especially when we cast aside all possibility (within our ontology) of the "reality" of the physical world? Without the physical world to act as a "selection" mechanism for what is "Real", why the bias for integers? This has been a question that I have tried to get answered to no avail.I think Bruno gives such high status to the natural numbers becausethey are perhaps the least-doubt-able mathematical entities there are.The very fact that talks of a "set-theoretic multiverse" exist makesone ask, how real are sets? Do set theories tell us more about ourminds than they do about the mathematical world? (Obviously, as DavidLewis pointed out, you need something like a set theory in order to domathematics at all, and as Russell says, for the average mathematicianit really doesn't matter.)

`My skeptisism centers on the ambiguity of the metric that defines`

`"the least-doubt-able mathematical entities there are". We operate as if`

`there is a clear domain of meaning to this phrase and yet are free to`

`range outside it at will without self-contradiction. Set theory, whether`

`implicit of explicitly acknowledged seems to be a requirement for`

`communication of the 1st person content. Is it necessary for`

`consciousness itself? Might consciousness, boiled down to its essence,`

`be the act of making a distinction itself?`

Also: *No one here has questioned the reality of the physical world.*Should I append this statement to every email until you stopcountering it?

`I frankly have to explicitly mention this because the "reality of`

`the physical world" is, in fact, being questioned by many posters on`

`this list. That you would write this remark is puzzling to me. I think`

`that I can safely assume that you have read Bruno's papers... Maybe the`

`problem is that I fail to see how reducing the physical world to the`

`epiphenomena of numbers does not also remove its "reality".`

This is the origin of Bruno's claim that COMP entails that physics is not computable, a corrolory of which is that Digital Physics is refuted (since DP=>COMP).Does the symbol "=>" mean "implies"? I get confused ...Yes, that is the usual meaning. It can also be written (DP or not COMP)."=>" = "or not"] Actually "a implies b" is defined as "not a or b".

`Thank you for this clarification! Would you care to elaborate on`

`this definition?`

-- Onward! Stephen "Nature, to be commanded, must be obeyed." ~ Francis Bacon -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.